A coin had tossed three times. Let: $X$-number of tails $Y$-number of heads
Find the expected value and variance $Z=XY$
My solution: $E(Z)=E(XY)= 2 \cdot 1/4 + 3 \cdot 1/4=6/4$ Because, I know that $ X,Y=0,1,2,3$ so, $Z=2,3$, since $Z=0,1$ doesn't describe three throws. And: $E(Z^2)=13/4$